Problem: Solve for $n$, $ -\dfrac{5}{4n} = -\dfrac{4}{20n} - \dfrac{n + 6}{4n} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4n$ $20n$ and $4n$ The common denominator is $20n$ To get $20n$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{5}{4n} \times \dfrac{5}{5} = -\dfrac{25}{20n} $ The denominator of the second term is already $20n$ , so we don't need to change it. To get $20n$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{n + 6}{4n} \times \dfrac{5}{5} = -\dfrac{5n + 30}{20n} $ This give us: $ -\dfrac{25}{20n} = -\dfrac{4}{20n} - \dfrac{5n + 30}{20n} $ If we multiply both sides of the equation by $20n$ , we get: $ -25 = -4 - 5n - 30$ $ -25 = -5n - 34$ $ 9 = -5n $ $ n = -\dfrac{9}{5}$